This varies from LL to LL, the best course of action is just to ask. Have a realistic idea of what terms you think are reasonable and don't be pushy about it. The demand for good housing far exceeds the supply but if you are particularly pleasant and make yourself a desirable tenant LL's may find it worth negotiating to keep you around.
But when in doubt, go to your realtor. Ideally they're fabulous people who would love to help answer your questions :)